The overarching goal of this project is to improve math and science education by adapting FluidMath, an embodiment of our novel concept of mathematical sketching, for high school math and science curricula. Using FluidMath, students and teachers can naturally enter symbolic mathematics expressions and supporting diagrams using a stylus-equipped computer (e.g. Tablet PC or electronic whiteboard). By automatically recognizing these handwritten notations and inferring relevant associations, FluidMath makes user notations come alive as interactive animations, virtual manipulatives, and dynamic graphs. When presented with early prototypes, a pilot group of teachers uniformly professed to a vision that FluidMath could transform the way mathematics is presented in their classrooms, and could be pivotal in both engaging student attention and deepening student comprehension. In particular, they observed that FluidMath offered a potential for rapidly and effectively exploring 2D and 3D functions, which students often have difficulty grasping, that they did not feel was attainable with existing technologies. Since the feasibility of FluidMath's underlying recognition technology has been successfully demonstrated as part of an NSF STTR project, the research challenge of this Phase I SBIR is to develop a detailed blueprint for how teachers can use FluidMath to achieve their classroom visions. The process will be to deploy FluidMath prototypes to a select, small group of teachers and then to dissect their usage scenarios, methodologies, and representative examples. Additionally, this process will require rapidly prototyping extensions to FluidMath that specifically address each teacher's emerging functional requirements for their curriculum and classroom workflow. Toward the end of Phase I, pilot tests of between-subjects evaluation procedures for gauging the educational efficacy of FluidMath will be conducted at one or two schools in which the same instructor will teach different classes with and without using FluidMath. Phase II of this SBIR will build upon the Phase I results to perform an expanded didactic evaluation of FluidMath with a wider group of teachers. These teachers will likely rely on the usage blueprints derived from Phase I. Project Narrative: The research conducted in this project will help to develop effective instructional technologies for mathematics and science education and will provide a foundation for exploring how the mathematical sketching concept can improve the learning process. [unreadable] [unreadable] [unreadable]